For a simple closed$-$loop path$*$ in a conservative field,

$*$That means the particle move around the loop and come back to the starting point.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=0$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=1$

cannot be evaluate

$$ is undefinited